Problem: Reduce to lowest terms: $- \dfrac{3}{7} \div \dfrac{8}{7} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{8}{7}$ is $ \dfrac{7}{8}$ Therefore: $ - \dfrac{3}{7} \div \dfrac{8}{7} = - \dfrac{3}{7} \times \dfrac{7}{8} $ $ \phantom{- \dfrac{3}{7} \times \dfrac{7}{8}} = \dfrac{-3 \times 7}{7 \times 8} $ $ \phantom{- \dfrac{3}{7} \times \dfrac{7}{8}} = \dfrac{-21}{56} $ The numerator and denominator have a common divisor of $7$, so we can simplify: $ \dfrac{-21}{56} = \dfrac{-21 \div 7}{56 \div 7} = -\dfrac{3}{8} $